In practical communication systems power amplifiers (PA) are commonly used to enable wireless transmission over long distances. When using such a PA, it is crucial to keep the input signal's power within the PA's linear region in order to avoid saturation of the transmitted signal, which leads to both in-band and out-band disturbances. Transmission signals at the PA input are therefore backed-off (BO) so that instantaneous high peak power values will not cause saturation. The cost of the BO is that the average power of the signal is lower, thus compromising the transmission rate. This effect is especially severe in transmission signals with wide dynamic range, such as OFDM. However, in band limited single carrier transmission, which is common in satellite communication systems, high Peak to Average Power Ratio (PAPR) is also common. The PAPR problem in satellite communication is significant due to the high cost of PA, and due to the limited satellite resources where even 1 dB loss is critical.
Since the length of the pulse shape exceeds the symbol duration, high instantaneous peak power values are the result of certain symbol sequences. A possible approach to reduce the PAPR is therefore to try to avoid such sequences.
For example, the method of Trellis shaping (TS), first suggested by Forney to reduce the average transmission power in high orders constellation signaling [1], has been shown to be useful for the purpose of PAPR reduction as well [2]. Originally, TS was shown to work well with Trellis Coded Modulation (TCM) [1]. Several attempts have been made to combine TS with other ECC schemes [3] [5]. In [5], LDPC code as inner code was combined with TS for power reduction. In [3] TS for PAPR reduction was combined with convolutional ECC. The reported gain in [3] was 1.8 dB PAPR gain with 1.5 dB loss in SNR, resulting in an overall link gain of 0.3 dB. However, the SNR loss was calculated theoretically and may be higher in practical schemes. Additionally, the information rate was 1 bit/symbol, and higher rates were not investigated.
TS is based on adding shaping bits, usually one bit per symbol, to create redundancy in the possible symbol sequences representing a given information word, and a Viterbi decoder which is used to select the symbol sequence with the minimal PAPR cost. Although PAPR gain can be achieved in this way, several issues are not fully addressed by PAPR reduction using TS. First, TS adds an integer number of bits per symbol, which does not allow a complete rate/shaping trade-off. Second, it is not clear whether the PAPR reduction achieved by TS for a given rate is optimal. And third, the combination of TS with modern error correcting codes (ECC) such as Turbo codes or LDPC, which is crucial for enabling a reliable communication system, has not been optimized, leading to lower gain.
In [4] a different approach is presented, in which certain symbol sequences that result in high PAPR, are simply forbidden by the transmitter. This constraint imposes a Markovian distribution on the transmission with a flexible rate to PAPR reduction trade-off, and is shown to theoretically achieve good PAPR reduction with low rate loss. A previous work by the authors [9] was an attempt to obtain a power reduction gain by trying to apply another distribution on transmission, with different probabilities of using certain symbol sequences.